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28. Solve each of the following equations by completing the square. (a) 2 x2 +3 x —4=0.

(c) 3 x2 – X – 10=0. (6) 7 x2—8 x–9=0.

(d) Væ+1+x=11. 29. The solutions of the quadratic equation for a problem do not always both satisfy the problem itself. Explain this. Examine to see whether it is illustrated in the working of the following problem:

Find the positive integer such that the square of it added to six times the number gives 27.

30. Explain how one goes to work to draw the graph of a given quadratic equation.

31. In how many points must the graph of a quadratic cut the XX axis in case the two solutions are real? What happens to the 'graph in case the two solutions are imaginary? Give simple illustrations.

32. What especial interest attaches to the points mentioned in Ex. 31 in case such points are present ?

33. Draw the graph of the quadratic x2—4 x=0.

34. The sum of two numbers is 29 and the sum of their squares is 505. Find the numbers.

35. A string is just long enough to go around a certain square. If 3 feet are cut off the string, it will then just reach round a square whose area is 4 that of the first square. How long is the string ?

For further exercises on this Chapter, see Appendix, p. 310.

APPENDIX

PART I. SUPPLEMENTARY EXERCISES

These exercises are intended as a supplement to those given in the body of the text. They may be used, at the discretion of the teacher, either for additional drill exercises during the first study of a topic, or for reviews.

SUPPLEMENTARY EXERCISES ON § 3 1. Envelopes which cost 7 cents a package at wholesale are sold for 3 cents more a package at retail; what is the retail price?

2. If the envelopes cost c cents a package at wholesale and are sold at retail for r cents more, what represents the retail price?

3. What is the retail price in Ex. 2 if c=6 cents, and r=3 cents? if c=51 cents, and r=2 cents?

4. One man walks 15 miles in one day and another man walks 3 miles more in the same time. How far did the second man walk in one day?

5. If the first man walked b miles and the other walked e miles more in the same time, how far did the second man walk in one day?

6. In Ex. 5, how far did the second man walk if b=20, and e=6? if b=19, and e=3?

7. How many minutes in 3 hours? in d hours ? in e hours? 8. Give the expression representing r more than 5. 9. If n=8, what is the value of 16+n? of 25+n? 10. Give the expression representing 5 less than k. 11. If c=17, what is the value of 20-c? of 36-c? 12. What is the next even number after 22?

13. If x is an even number, what represents the next even number after it?

14. If a boy is 13 years old now, how old will he be in 3 years? If he is x years old now, how old will he be in 3 years?

15. If a man's present age is represented by 2, what represents his age 10 years ago?

16. What is the cost of 6 railway tickets at 75 cents each? What is the cost of x railway tickets at 75 cents each?

17. If a suit of clothes costs 9 times as much as a hat, and if the hat costs k dollars, what represents the cost of the suit? What represents the cost of both ?

18. A baseball team scores 27 runs in 9 innings. What was the average per inning?

19. A baseball team scores y runs in 9 innings. What was their average per inning?

20. If a team scores 6 runs in y innings, what is its average per inning?

21. If I spend 40 cents to-day and r cents to-morrow, how much shall I spend in the two days?

22. If one part of 10 is 7, what is the other part? 23. If one part of a is 3, what is the other part? 24. If one part of 10 is a, what is the other part?

25. If x is the greater part of a number and the difference between the parts is 4, what is the other part?

26. If y is the smaller part of a number and if the smaller part is 4 less than the larger, what is the larger?

27. What is the expression showing how much 6 a exceeds 13?

28. John has 3 times as much money as James, and James has 4 times as much money as Harry. If Harry has x dollars, how much has each of the others ?

SUPPLEMENTARY EXERCISES ON $$ 6–13 Solve each of the following equations. 1. x+4=20.

8. x=22—x. 15. 1 x+2=8. 2. <—6=32.

9. 3 x-10=2 x. 16. x+6=18. 3. x+12=17. 10. 5 x=21+2 x. 17. i x-12=6. 4. 2 x–8=16. 11. x=35–6 x. 18. x+5 x=8+10. 5. 3 x+18=42. 12. 4 x–2 x=18. 19. 2 x+5=6. 6. 5x-10=40. 13. 5 x=29–4. 20. 3 x-4=18. 7. 2 x=20-3x. 14. { x=10.

SUPPLEMENTARY EXERCISES ON 88 16-17

1. Give the negative (or antonym) of (a) sunrise, (b) to hoist the flag; (c) clean; (d) to increase; (e) overhead.

Add the following:
2. +16 7. +15

-122
+ 8
+32

13. +174
-36

-100

+ 22

+36 8. +19

+[ + [

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+ IT + [T |

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-18

10. +3.7

-5.7 11. -8.36

+2.15

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-42

-17 16. -81

-74

-12

-97 +96

+42

SUPPLEMENTARY EXERCISES ON $$ 18-20 Find the value of each of the following expressions. 1. 6+(-2)+(-1).

s. 17+25+(-42). 2. -4+ -3)+7.

7. -19+(-27)+(-13). 3. 9+(-8)+(-10).

8. 36+(-19)+-1). 4. -6+-7)+(-8).

. 28+14+36. 5. -18+12+(-4).

10. -28+-14)+(-36). 11. -3713. -2016. - 1 17. 126 19. -42

15.
+14
-132

3 6
18
-36

134 -10

-130 -15

-28

+23

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[blocks in formation]

14. -15

-18 +31

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18

- 7

=50

-124

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